# Projection-Free Bandit Convex Optimization

@inproceedings{Chen2019ProjectionFreeBC, title={Projection-Free Bandit Convex Optimization}, author={Lin Chen and Mingrui Zhang and Amin Karbasi}, booktitle={AISTATS}, year={2019} }

In this paper, we propose the first computationally efficient projection-free algorithm for bandit convex optimization (BCO). We show that our algorithm achieves a sublinear regret of $O(nT^{4/5})$ (where $T$ is the horizon and $n$ is the dimension) for any bounded convex functions with uniformly bounded gradients. We also evaluate the performance of our algorithm against baselines on both synthetic and real data sets for quadratic programming, portfolio selection and matrix completion problems… Expand

#### 16 Citations

Projection-Free Bandit Optimization with Privacy Guarantees

- Computer Science, Mathematics
- AAAI
- 2021

This is the first differentially-private algorithm for projection-free bandit optimization, and in fact its bound matches the best known non-private projection- free algorithm and the bestknown private algorithm, even for the weaker setting when projections are available. Expand

Improved Regret Bounds for Projection-free Bandit Convex Optimization

- Computer Science, Mathematics
- AISTATS
- 2020

The challenge of designing online algorithms for the bandit convex optimization problem (BCO) is revisited and the first such algorithm that attains expected regret is presented, using only overall calls to the linear optimization oracle, in expectation, where T is the number of prediction rounds. Expand

Structured Projection-free Online Convex Optimization with Multi-point Bandit Feedback

- 2021

We consider structured online convex optimization (OCO) with bandit feedback, where either the loss function is smooth or the constraint set is strongly convex. Projectionfree methods are among the… Expand

Projection-free Online Learning over Strongly Convex Sets

- Computer Science, Mathematics
- AAAI
- 2021

This paper proves that OFW enjoys a better regret bound of $O(T^{2/3})$ for general convex losses and proposes a strongly convex variant of OFW by redefining the surrogate loss function in OFW. Expand

An Optimal Algorithm for Bandit Convex Optimization with Strongly-Convex and Smooth Loss

- Mathematics, Computer Science
- AISTATS
- 2020

This study introduces an algorithm that achieves an optimal regret bound of Õ(d √ T ) under a mild assumption, without self-concordant barriers, for non-stochastic bandit convex optimization with strongly-convex and smooth loss functions. Expand

Optimal Regret Algorithm for Pseudo-1d Bandit Convex Optimization

- Computer Science
- ICML
- 2021

A new algorithm OPTPBCO is proposed that combines randomized online gradient descent with a kernelized exponential weights method to exploit the pseudo-1d structure effectively, guaranteeing the optimal regret bound mentioned above, up to additional logarithmic factors. Expand

Projection-free Online Learning in Dynamic Environments

- Computer Science
- AAAI
- 2021

This paper improves an existing projection-free algorithm called online conditional gradient (OCG) to enjoy small dynamic regret bounds with the prior knowledge of VT, and achieves an O(max{T V 1/3 T , √ T}) dynamic regret bound for convex functions and an O (max{ √ TVT log T , log T} dynamic regret Bound for strongly conveX functions. Expand

Online Continuous Submodular Maximization: From Full-Information to Bandit Feedback

- Computer Science, Mathematics
- NeurIPS
- 2019

Bandit-Frank-Wolfe is the first bandit algorithm for continuous DR-submodular maximization, which achieves a $(1-1/e)-regret bound of $O(T^{8/9})$ in the responsive bandit setting. Expand

Projection-free Distributed Online Learning with Strongly Convex Losses

- Computer Science, Mathematics
- ArXiv
- 2021

It is demonstrated that the regret of distributed online algorithms with C communication rounds has a lower bound of Ω(T/C), even when the loss functions are strongly convex, which implies that the O(T ) communication complexity of the proposed algorithm is nearly optimal for obtaining the O (T 2/3 log T ) regret bound up to polylogarithmic factors. Expand

Online Boosting with Bandit Feedback

- Computer Science, Mathematics
- ALT
- 2021

An efficient regret minimization method is given that has two implications: an online boosting algorithm with noisy multi-point bandit feedback, and a new projection-free online convex optimization algorithm with stochastic gradient that improves state-of-the-art guarantees in terms of efficiency. Expand

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